OFFSET
0,2
COMMENTS
a(n-1) (with a(-1) = 0) appears in the formula for 1/rho(11)^n, n >= 0, with rho(11) = 2*cos(Pi/11) (the length ratio (smallest diagonal)/side in the regular 11-gon), when written in the power basis of the degree 5 number field Q(rho(11)): 1/rho(11)^n = A038342(n)*1 + A230080*rho(11) - A230081(n)*rho(11)^2 - a(n-1)*rho(11)^3 + A038342(n-1)* rho(11)^4, n >= 0, with A038342(-1) = 0. See A230080 with the example for n=4. - Wolfdieter Lang, Nov 04 2013
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,3,-4,-1,1).
FORMULA
G.f.:(1-x)/(1-x^5+x^4+4*x^3-3*x^2-3*x). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009
a(n) = 3*a(n-1) + 3*a(n-2) - 4*a(n-3) - a(n-4) + a(n-5), n >= 0, with a(-5)=0, a(-4)=-1, a(-3)=a(-2)=a(-1)=0. - Wolfdieter Lang, Nov 04 2013
MATHEMATICA
LinearRecurrence[{3, 3, -4, -1, 1}, {1, 2, 9, 29, 105}, 30] (* Harvey P. Dale, Apr 16 2015 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 02 2002
EXTENSIONS
Edited by Henry Bottomley, May 06 2002
STATUS
approved